Graphing and Solving Inequalities/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby. A cluster of balloons floats through the sky, with two lawn chairs dangling from it. Tim and Moby sit in the chairs. TIM: Are you sure you know what you’re doing? MOBY: Beep. Moby holds up a book titled: Whimsical Cluster Ballooning FAQs. TIM: How are we supposed to get back down? MOBY: Beep. Moby pulls out a pea shooter, and bursts one of the balloons. The chairs abruptly drop a few feet. TIM: And how do we go higher? Moby holds up a 10 kilogram weight, which is hanging from his chair by a rope. He also holds up a pair of scissors. TIM: I hope we can cut enough weight to get over that. A mountain looms in front of Tim and Moby. Tim reads from a typed letter. TIM: Dear Tim and Moby, how do you solve an inequality? From, Matt. Solving an inequality is a lot like solving a regular equation. Just about all of the same rules apply. On-screen, an equation appears, reading, "x plus 3 equals 5." TIM: The difference is that an inequality shows the relationship between quantities that are not equal. On-screen, the equals sign is crossed out. TIM: Inequalities use symbols like greater than, less than, greater than or equal to, and less than or equal to. On-screen, the four mathematical symbols appear: greater than; less than; greater than or equal to; and less than or equal to. Each of them replaces the equals sign in the previous equation x plus 3 equals 5. TIM: Matter of fact, we’ve got ourselves a little inequality staring us in the face right now. We’re cruising along at uh… MOBY: Beep. Moby displays their altitude on his internal computer. It reads, 1190 meters. TIM: Right, 1190 meters above sea level. And that mountain up ahead is 1315 meters high. Tim and Moby’s altitude, which is 1190 meters, is displayed. The mountain's altitude, which is 1315 meters, is also displayed TIM: We know that 1190 is less than 1315. On-screen, an inequality reads, "1190 is less than 1315." TIM: The question is, how many meters do we need to add to our height so that it’s greater than the mountain’s? On-screen, the inequality changes to "x plus 1190 is greater than 1315." The greater than sign is highlighted. MOBY: Beep. TIM: That x is a variable, an unknown amount represented by a letter. On-screen, the inequality "x plus 1190 is less than 1315 appears." The x, is highlighted. TIM: To solve an inequality, you isolate the variable, just as if you were solving a regular equation. In our case, that means subtracting 1190 from the left side of the formula. But like in an equation, whatever you do to one side of the equation, you have to do to the other. On-screen, the inequality changes to "x plus 1190, minus 1190, is greater than 1315 minus 1190." TIM: You can do the same kind of thing with addition, multiplication, or division, depending on the problem. On-screen, a plus sign, a multiplication sign, and a division sign appear. TIM: Now, let's solve our inequality. Tim mumbles while solving the inequality in his head. On-screen, 1190 is shown being subtracted from both sides of the inequality "x plus 1190 is greater than 1315" to get "x plus zero is greater than 125" and then finally "x is greater than 125." TIM: X is greater than 125. So, we need to climb more than 125 meters to clear that mountain! We can graph our inequality on a number line this way. On-screen, a number line appears. The lowest number, on the left, is negative 75. The highest number, on the right, is 175. A red circle appears around the 125 mark on the number line. A red arrow points right, from the open circle all the way to the right end of the number line. TIM: See? The red line starts at 125 and points upward into infinity. That means x is greater than 125. On-screen, the text above the inequality reads, "x is greater than 125." TIM: If x were greater than or equal to 125, we’d just fill in the circle. On-screen, the inequality changes to "x is greater than or equal to 125." The red circle at 125 is filled in. TIM: See? Moby nods. Tim leafs through the Whimsical Cluster Ballooning FAQs. TIM: Now, according to this, we rise one meter for every kilogram of weight we dump. So we need to dump more than 125 kilograms. MOBY: Beep. TIM: There’s only 120 kilograms of ballast? That means we’ll be five meters short! MOBY: Beep. Moby salutes and leaps out of his chair, sacrificing himself so Tim won't hit the mountain. TIM: No, wait a second! Tim pulls a dumbbell out of his backpack. TIM: I forgot to mention, I brought my weights along. Moby rises up into the air, as rocket powered jets fire from his heels. He hovers angrily in midair with his hands on his hips. MOBY: Beep! TIM: I don’t know. You said it’d be a long trip, and I thought I might pass the time with some exercise. Tim starts doing bicep curls with the dumbbell. Moby is peeved. MOBY: Beep! TIM: Fine. I suppose you're gonna tell me that we're not going bowling, either. Tim pulls a bowling ball from his backpack and smiles sheepishly. Category:BrainPOP Transcripts